Abstract: We present an implementation of time-dependent density functional
perturbation theory for spin fluctuations, based on planewaves and
pseudopotentials. We compute the dynamic spin susceptibility self-consistently
by solving the time-dependent Sternheimer equation, within the adiabatic local
density approximation to the exchange and correlation kernel. We demonstrate
our implementation by calculating the spin susceptibility of representative
elemental transition metals, namely bcc Fe, fcc Ni and bcc Cr. The calculated
magnon dispersion relations of Fe and Ni are in agreement with previous work.
The calculated spin susceptibility of Cr exhibits a soft-paramagnon
instability, indicating the tendency of the Cr spins to condense in a
incommensurate spin density wave phase, in agreement with experiment.